Installing a light switch

I'm converting a shed to an office and previously off one "cable" there were lights and sockets. We have had to remove some wires and are starting from a pretty basic point.
We have wired in a Plug Socket using the solitary cable coming into the building, can we run power from this socket to a light switch and then onto the light itself?

nope.

do a search for, power to shed, garage outbuilding etc, there is a lot more to it and has been done 722 times

If you put a fused spur next to it and fuse it at 3a you can then run the load side of the fused spur to your light fitting- this uses the fused spurs switch as the lights on / off.

External electrics is more prone to issues and is Part P works. Hopefully your cable route to the main house is safe and suitable for use, with RCD fuse protection and cable correct for the weathering and wetting it may suffer.